If $OA$ and $OB$ are the tangents to the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ drawn from the origin $O$,then $AB =$

The line $3x-y+k=0$ touches the circle $x^2+y^2+4x-6y+3=0$. If $k_1, k_2$ $(k_1 < k_2)$ are the two values of $k$,then the equation of the chord of contact of the point $(k_1, k_2)$ with respect to the given circle is

The length of the chord of contact of tangents drawn from the point $(4,4)$ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ is: (in $\sqrt{2}$)

The area of the triangle (in sq. units) formed by the tangents drawn from $P(4,4)$ to the circle $S \equiv x^2+y^2-2x-2y-7=0$ and the chord of contact of $P$ with respect to $S=0$ is

Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$,then $AB=$

Two circles centered at $(2,3)$ and $(5,6)$ intersect each other. If the radii are equal,the equation of the common chord is